Is this sentence grammatically wrong?

Yes, yes, it is wrong.

The modifier is misplaced.

You aren't taking your dog.

And you aren't taking a bath.

The dog is taking a bath.

You're giving the dog the bath it's taking.

It's like saying, "Throw the horse over the fence some hay."

A person could say "I took a bath." meaning he had bathed, but animals cannot bathe themselves so you can only say you give/ gave a dog a bath or you bathe/ bathed the dog. I have put it in both present and past tense.

Yes. Try, I gave my dog a bath or My dog took a bath.

Yes it is wrong. The correct way to say this sentence is: I gave my dog a bath.

It is so wrong I don't even know where to begin! Are you serious?

How about:

"I gave my dog a bath." or

"I took my dog to the groomer for a bath."

i took my dog for a bath?

If you mean you carried a bath to your dog then it is fine. If this is not what you mean, then no.

it should be

i took my dog for a bath

or

i took my dog to bath

Yes, very wrong indeed.